f(x)=sinx-cosx=√2sin(x-4/π)
(1).T=2π
(2).f(x)max=√2f(x)min=-√2
(3).sina+cosa=√2cos(a-π/4)
cos(a-π/4)=√[1-sin²(a-π/4)]
sin²(a-π/4)=[f(a)/√2]²=1/32a∈（0,π/2）所以（a-π/4）∈（-π/4,π/4）
所以cos(a-π/4)=√31/32
所以sina+cosa=√2cos(a-π/4)=√62/32